Integer points on the elliptic curve with Fibonacci numbers

A set { a 1 , a 2 , ⋯ , a m } of positive integers is called Diophantine m -tuple if a i a j + 1 is a perfect square for all 1 ≤ i < j ≤ m . In this paper, we find the structure of torsion group of elliptic curve E k induced by the Diophantine triple { F 2 k , F 2 k + 4 , 5 F 2 k + 2 } constructe...

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Bibliographic Details
Published in:Indian journal of pure and applied mathematics 2024-06, Vol.55 (2), p.480-488
Main Author: Park, Jinseo
Format: Article
Language:English
Subjects:
Applications of Mathematics
Curves
Fibonacci numbers
Integers
Mathematics
Mathematics and Statistics
Numerical Analysis
Original Research
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Summary:A set { a 1 , a 2 , ⋯ , a m } of positive integers is called Diophantine m -tuple if a i a j + 1 is a perfect square for all 1 ≤ i < j ≤ m . In this paper, we find the structure of torsion group of elliptic curve E k induced by the Diophantine triple { F 2 k , F 2 k + 4 , 5 F 2 k + 2 } constructed by Fibonacci numbers, and find all integer points on E k under assumption that rank ( E k ( Q ) ) = 1 .
ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-023-00378-2